LONDON (Reuters) - Arqiva, a company that runs much of Britain's TV and mobile infrastructure but is little known outside the industry, could put itself up for sale or list on the stock market as part of a review led by Rothschild, two sources said on Wednesday.

Arqiva, which carried the BBC's first TV broadcast in 1936, works with major mobile operators, independent radio groups and leading British broadcasters. Its biggest shareholders include the Canada Pension Plan Investment Board and Macquarie.

Media reports have suggested the firm could be worth between 5 and 6 billion pounds ($7.57 billion). With revenues in the year to end June 2016 of 850 million pounds, Arqiva could draw interest from other large pension funds, sovereign investors and private equity groups attracted to its predictable cash flow, as well as telecom towers operators in Europe and the United States.

Prime Minister Theresa May's government has signaled it would take a more cautious approach in future over foreign investment in "critical infrastructure" after it initially put a major nuclear deal with Chinese investors on hold last year, saying it needed more time to assess it.

Chinese investors have shown they are willing to invest billions in British infrastructure and Chinese network equipment maker Huawei is already a key player in Britain's telecoms sector, working with fixed and mobile operators.

The first source, who declined to be named because the talks are not public, said the company was still weighing its next move and had not taken any final decisions.

The second source said a market flotation remained an option due to "lukewarm" interest from potential bidders for broadcasting towers. They said the process was at an early stage and no formal talks have been held with possible bidders.

With industry players such as Cellnex and American Tower focusing on mobile towers, the source said it made sense to see if there would be more value in a stock listing for a firm that combines mobile and TV assets.

Arqiva declined to comment while Rothschild [ROT.UL] was not immediately available to comment.